THE IMPACTS OF CONGESTION ON COMMERCIAL VEHICLE TOUR CHARACTERISTICS AND COSTS

Transcription

1 Figliozzi 1 THE IMPACTS OF CONGESTION ON COMMERCIAL VEHICLE TOUR CHARACTERISTICS AND COSTS Miguel Andes Figliozzi Depatment of Civil and Envionmental Engineeing Maseeh College of Engineeing and Compute Science Potland State Univesity figliozzi@pdx.edu ABSTRACT Analytical modeling and insights, numeical expeiments, and eal-wold tou data ae used to undestand the impact of congestion on uban tou chaacteistics, caies costs, and distance/time taveled. This pape categoizes tous into thee classes based on thei tou efficiency and vaiable costs stuctue. Tavel time/distance between customes and depot is found to be a cucial facto that exacebates the negative impacts of congestion. Tavel time vaiability is a significant facto only when tavel time between depot and customes is consideable in elation to the maximum tou duation. Fo each custome, it is possible to define a dimensionless coefficient that povides an indication of the elative impact of congestion on outing constaints. Congestion also affects caies cost stuctue, as congestion wosens the elative weight of wages and ovetime escalates and the elative weight of distance elated costs decease. KEYWORDS: Congestion Modeling, Caie Costs, Uban Feight, City Logistics

2 Figliozzi 2 1. Intoduction Inceased tavel times and the uncetainty bought about by congestion impacts the efficiency of logistics opeations. Diect and indiect costs associated with congestion have been widely studied and epoted. Most of the studies have focused on passenges value of tavel time, shippes value of time and maket access costs, poduction costs, and labo poductivity costs (Weisbod et al., 2001). Howeve, the modeling and study of the specific impacts of uban congestion on commecial vehicle tous have eceived scant attention. The lack of studies is lagely explained by lack of disaggegated and compehensive commecial vehicle data, which due to pivacy o competitive easons, is expensive to collect o unattainable at the desied level of detail. This eseach studies the impact of congestion on commecial vehicle tous in an uban aea. It contibutes to the undestanding of the impacts of congestion on commecial vehicle tous. The specific contibutions of this eseach ae theefold: a) it analytical appoximations and empiical data to study and descibe the impact of congestion on tou chaacteistics, b) it discusses congestion costs fom a caie s pespective, c) it uses a novel and intuitive classification of uban distibution tous accoding to thei efficiency and susceptibility to congestion. Empiical o eal-wold disaggegated tou data is also analyzed to validate analytical insights of the model. Recent studies indicate that a high popotion of uban commecial vehicle kilometes taveled (VKT) oiginate at distibution centes (DC), waehouses, o depots (Cambidge Systematics, 2003, Outwate et al., 2005) and constitute tip-chains o multi-stop tous. Multi-stop commecial vehicle tous ae ubiquitous in uban aeas; fo example, in Denve appoximately 50% of single and combination tuck tous include 5 to 23 stops pe tou (Holguin-Veas and Patil, 2005). The tems oute, tou, and tipchain ae used intechangeably in this eseach to designate the activity of a commecial vehicle that stats at a depot, visits one o moe customes, and then etuns to the depot; fo the sake of bevity the wod tou is used heein.

3 Figliozzi 3 The eseach is oganized as follows: section two povides a liteatue eview of congestion impacts on caie opeations and costs. Section thee intoduces a model to analyze the impacts of congestion on commecial vehicle tous. Section fou pesents analytical insights fo time constained tous. Section five contains a numeical analysis and discusses tou efficiency. Section six discusses the impact of congestion on caies costs. Section seven examines empiical tou data; it also poposes a classification of tous based on thei efficiency and vulneability to congestion. Section eight ends with conclusions. 2. Liteatue Review It is widely ecognized that congestion seiously affects logistics opeations. McKinnon (1999) pesents the esults of in-depth inteviews with DC manages and discusses the negative effects of congestion on logistics opeations. Diect and indiect costs of congestion on passenges tavel time, shippes tavel time and maket access, poduction, and labo poductivity have been widely studied and epoted. Fo a systematic eview of this congestion liteatue the eade is efeed to the wok of Weisbod et al. (2001). Sizeable pogess has been made in the development of econometic techniques to study the joint behavio of caies and shippes in egads to congestion (Henshe and Puckett, 2005). Suvey esults suggest that the type of feight opeation has a significant influence on how congestion affects caies opeations and costs. Data fom a Califonia suvey indicate that congestion is peceived as a seious poblem fo companies specializing in LTL (less-than-tuckload), efigeated, and intemodal cago (Golob and Regan, 2001). In addition, Golob and Regan (2003) found a positive elationship between the level of local congestion and the puchase of outing softwae. Caies that do not follow egula outes, e.g. fo-hie caies, tend to place a highe value on the usage of eal-time infomation to mitigate the effects of congestion (Golob and Regan, 2005). Anothe banch of the liteatue models the elationship between industial/commecial pocuement and congestion. The impact of just-in-time (JIT) poduction systems, i.e. moe tips with smalle shipment sizes, on vehicle tip geneation has been analyzed and modeled (Rao et al., 1991, Moinzadeh et al.,

4 Figliozzi ). Using data fom Auckland, New Zealand, Sankaan et al (2005) study the impact of congestion and eplenishment ode sizes on caies with time-definite deliveies. Sankaan and Wood (2007) continues this wok and pesents a model using Daganzo s (1984, 1991) appoximations to outing poblems. Fo poblems whee outes have 10 o moe deliveies Sankaan and Wood (2007) indicate that congestion costs incease with the aveage numbe of ounds pe day and decease with the wokday duation, the squae oot of the numbe of deliveies, and that congestion is invaiant with fixed o vaiable stop times. Routing constaints limit the numbe and chaacteistics of the feasible set of tous that caies can use to meet custome demand. Figliozzi (2006) models tou constaints using Daganzo s (1991) appoximations to outing poblems and analyzes how constaints and custome sevice time affect tip geneation using a tou classification based on supply chain chaacteistics and oute constaints. Building on this wok, Figliozzi (2007) poposes an analytical famewok to study the impact of policy o netwok changes on uban feight VKT; the model shows that a decease in tavel speed seveely affects tous with time window constaints while capacity constained tous ae less affected. Figliozzi (Figliozzi, 2007) also indicates that changes in both VKT and vehicle hous taveled (VHT) diffe by type of tou and outing constaint. This wok links the dominant tou constaints to the time sensitivity of the commecial activity and the value of the activity itself in elation to the cost of tanspot to define fou tou types: (1) capacity constained tous, (2) fequency of sevice constained tous, (3) tou duation constained tous, and (4) time window constained tous. It is established that tou duation and time window constained tous ae the most affected by congestion. Confidentiality issues ae usually an insumountable baie that pecludes the collection of detailed and complete feight data. To the best of the autho s knowledge, all feight congestion studies pesent aggegated tou data with the exception of Figliozzi et al. (2007) and Geaves and Figliozzi (2008). In these two studies detailed tuck activity was analyzed and disaggegated tou data was used to eveal tou chaacteistics, speed vaiability, and data collection challenges. Moe ecently, an analytical model to detemine the impact of time windows on vehicle outing tou was developed (Figliozzi, 2008b). To the

5 Figliozzi 5 best of the autho s knowledge, thee is no eseach whose majo focus is on the impact of congestion on vehicle outing tous costs and stuctue. Tanspotation agencies ae inceasingly using tavel time eliability as a congestion measue (Chen et al., 2003); eliability is often associated to a buffe time index (Lomax et al., 2003, Bemme et al., 2004). The buffe time index epesents the exta time a tavele needs to allow in ode to aive on time 95% of the time. Caies also use buffes to mitigate the effects of tavel time o demand vaiability. Reliability as a constaint o objective has also been incopoated in opeations eseach models whee outes and sevice aeas ae designed using continuous appoximations (Eea, 2000, Novaes et al., 2000) o on stochastic pogamming (Lapote and Louveaux, 1993, Kenyon and Moton, 2003). In paticula, Eea (2000) poposes continuous appoximations to estimate expected detou and distances in a stochastic vesion of the capacitated vehicle outing poblem. To the best of the autho s knowledge, no model has been developed to study the impacts of congestion on tou chaacteistics, costs, and VKT/VHT. 3. The Tou Model This eseach consides a system with one DC o depot and n customes. A tou is defined as the closed path that a tuck follows fom its depot to visit one o moe customes in a sequence befoe etuning to its depot duing a single dive shift. A tou is compised of seveal tips; a tip is defined by its oigin and destination and chaacteized by its distance and tavel time attibutes. A seminal contibution to the estimation of the length of a shotest closed path o tou though a set of points was established by Beadwood et al. (1959). Daganzo (1984) poposed a simple and intuitive fomula fo the capacitated vehicle outing poblem (CVRP) length when the depot is not necessaily located in the aea that contains the customes: ln ( ) = 2 n/ Q an

6 Figliozzi 6 In this expession lnis ( ) the total length of the CVRP poblem seving n customes, the aveage distance between the customes and the depot is, the aea that contains the customes is a, and the maximum numbe of customes that can be seved pe vehicle is Q. Daganzo s appoximation can be intepeted as having: (a) a tem elated to the distance between the depot and customes and (b) a tem elated to the distance between customes. An appoximation to the aveage length of vehicle outing poblems to seve n customes fo diffeent values of m is: n m ln ( ) = 2m+ kl an (1) n whee: ln: ( ) the total length of the tous needed to seve n customes n : the numbe of stops o customes m : the numbe of outes k l : coefficient to be estimated by linea egession a : the extent of the aea of sevice compised by the n customes : the aveage distance fom the depot to the n customes Expession (1) is a obust appoximation to pedict the aveage length of tous in a divese set of andomly geneated instances and empiical o eal-wold uban netwoks (Figliozzi, 2008c). This expession has been tested in compact squae aeas with diffeent pattens of custome spatial distibution, time windows, custome demands, and depot locations. The fit of expession (1) to simulated and empiical data is high with a -squae of 0.96 to 0.99 and a mean absolute pecentage eo (MAPE) of less than 5%. The value of the coefficient k l is detemined by linea egession and captues the influence of factos such as spatial custome distibution, depot location, and time windows. Expession (1) is minimized when m = 1, i.e. one oute seves all customes, and maximized when m= n, i.e. one oute pe custome.

7 Figliozzi 7 Let custome ii, I= {1,..., n} have a location x i and a distance i to the depot; distance between customes i, j I. The set of tous to seve all customes in I is denoted d ij epesents the R = {1,..., m}, whee m indicates the numbe of outes o sevice egions and n is the numbe of customes in oute R. Any given oute R is fomed by a set of n + 1 links denoted L = n + 1. Let: L, whee t u = Time to load/unload a unit of poduct t o = Fixed time when stopping at a custome t l = Aveage tavel time in link l f t l = Fee-flow tavel time in link l s = d / t = Aveage tavel speed in link l l l l f s l = Fee-flow tavel speed in link l α = Congestion incease coefficient s = Aveage tavel speed in any given oute σ l = Standad deviation of the tavel time in link l υ = σ / t = Coefficient of vaiation in link l l l l ρ kl = Coelation between the distibutions of tavel time in links k and l w = Tou duation constaint b = Vehicle capacity q = Amount deliveed at custome ii, I= {1,..., n} i q = Aveage amount deliveed pe custome in oute, such that nq b

8 Figliozzi 8 The units associated with each mathematical element ae clealy detemined by thei physical meaning, i.g. distance, time, aea, speed, etc. Coefficients ae simply dimensionless o have dimensions that ae detemined by the othe elements in the mathematical expession, e.g. k l in expession (1). Thee ae seveal constaints associated with the opeation of an uban commecial vehicle fleet: the type and capacity of the vehicles, dives woking hous o maximum tou duations, sevice time, and the design of balanced tous (Bodin et al., 2003). Fo a given set of custome equests, the fleet opeato delineates tous that satisfy these equests and constaints. In uban tous, commonly binding constaints fo sevice, package delivey, and LTL 1 tous ae sevice time (moning/aftenoon custome visits) and tou duation. A common assumption when continuous appoximations ae utilized is that outes ae balanced, i.e. outes have a simila numbe of customes (Daganzo, 1984, Daganzo, 1991). Assuming balanced outes, the binding constaint fo each oute with an aveage of n/ m customes and aveage speed s can be expessed as: 1 n m n n (2 + kl an ) + to + tu q w (2) s nm m m Although in pactice commecial vehicles do not expeience the same levels of congestion at all points in a oute, an aveage speed s is assumed fo the sake of analytical tactability. The tou duation can be limited by one o seveal constaints such as: a) sevice consideations, e.g. tou duations of less than eight hous to ensue deliveies duing nomal business hous, b) dive woking hous, e.g. by county o state law the numbe of consecutive hous that a tuck dive can dive is esticted, usually the theshold is between 10 and 12 consecutive hous, and c) cost consideations, e.g. afte a cetain numbe of hous the caie must pay ovetime, which can be a significant cost in congested aeas as discussed in Section 6. The tou effective speed, which also takes into account the time spent at customes, is defined as: 1 LTL stands fo less-than-tuckload

9 Figliozzi 9 s e = n m 2 + kl an nm 1 n m n n (2 + kl an ) + to + tu q s nm m m 4. Analysis of the Impact of Congestion on Duation Constained Tous To facilitate the analysis of congestion impacts, tous ae boken down into thee cases: (a) the incease in aveage tavel time, (b) the incease in tavel time vaiability, and (c) the inteaction effect between a simultaneous incease in aveage tavel time and vaiability. Pactically, the latte and most complicated case is usually the most elevant. Howeve, simple cases ae analyzed fistly fo the sake of pesentation efficiency Incease in aveage tavel time no uncetainty An incease in aveage tavel time can be expessed by the coefficient α 1 that eflects the tavel time incease with espect to the fee-flow tavel time: t l = α t and f l s l 1 s f l = (3) α By using this coefficient, expession (2) can be estated as: α n m n n (2 + kl an) + to + tu q w (4) s nm m m f If tavel time inceases and the tou duation constaint (4) is violated, the numbe of outes, m, inceases to estoe feasibility. Since the definition of VHT includes only time spent on the oad netwok, i.e. VHT does not include time spent at the customes, an incease in aveage tavel time inceases not only diving time but may also incease the numbe of tous and the total distance taveled. Theefoe, the diect impact on VHT alone is insufficient to descibe the effects of congestion; the impact on VKT

10 Figliozzi 10 must also be consideed. Fo any given α > 1, the pecentage-wise incease in VHT is, on aveage, always lage than the pecentage-wise incease in VKT. If pecentage time diving is calculated as the atio between time diving and tou duation, then an incease in aveage tavel time inceases the pecentage time diving wheeas the custome time, i.e. time spent at the customes, is unaffected Incease in tavel time vaiability If the tavel times ae not constant, the buffe σ z must be added to (2) in ode to guaantee a custome sevice level: 1 n m n n (2 + kl an ) + to + tu q w σ z (5) s nm m m Assuming nomally distibuted tavel times, the coefficient z is elated to the pobability of completing the tou within the allowed tou duation. The oute tavel time standad deviation can be expessed as: n n 2 = k + kl k l l = k+ 1 k, l L k L k= 1 l= k+ 1 (6) σ σ ρ σ σ Unlike pevious studies and modeling appoaches, the coelation between tavel times is included because empiical data suggests that a positive coelation may not be negligible (Figliozzi et al., 2007). To minimize costs, a caie will educe the numbe of vehicles needed as well as the total oute lengthduation without violating custome sevice constaints. Fo a given set of customes and depots, this is equivalent to minimizing the numbe of outes subject to constaint (5). The oute tavel time standad deviation, expession (6), gows with the numbe of customes pe oute o with an incease in vaiability (vaiances ae non-negative numbes). An incease in tavel time vaiability affects the ight-hand tem of expession (5) which is deceased by the tem σ z. This may

11 Figliozzi 11 lead to a violation of the constaint and theefoe m must incease in ode to estoe feasibility. Total oute duation vaiability inceases with espect to case (a) but aveage oute duations decease when the buffe incease makes expession (5) binding and m inceases. Hence, on aveage, oute duations shoten but the sum of the oute duation plus the buffe tends to emain constant. Unlike case (a), only when m inceases thee is an incease in distance taveled, time diving, and pecentage time diving. Aveage diving speed does not change. Howeve, effective tou speed, s e, inceases as the numbe of stops pe tou deceases Inteaction effect between a simultaneous incease in tavel time and vaiability If thee is an incease in congestion and aveage tavel time inceases while the coefficient of vaiation emains constant the impact of congestion is amplified. A widespead appoach to indicate the degee of uncetainty in the distibution of a andom vaiable is to calculate the coefficient of vaiation. Using coefficients of vaiation υ, expession (6) can be estated as: n n 2 = ( k tk) + kl ktk ltl l = k+ 1 k, l L k L k= 1 l= k+ 1 σ υ ρ υ υ Although in pactice commecial vehicles do not expeience the same levels of tavel time vaiability at all points in a oute, a constant coefficient of vaiation is assumed fo the sake of analytical tactability. Assuming a constant coefficient of vaiation, υ = υ = υ kl, L, then: k l n n 2 = tk + kltktl l = k + 1 k, l L k L k= 1 l= k+ 1 (7) σ υ ρ Expessing the tavel time using the fee-flow tavel times, t l = α t f l n n f 2 f f = ( tk ) + kltktl l = k+ 1 k, l L k L k= 1 l= k+ 1 (8) σ υα ρ f Denoting σ as the fee-flow standad deviation of the oute tavel time in oute

12 Figliozzi 12 σ n n f f 2 f f = ( tk ) + ρkltktl l = k+ 1 k, l L k L k= 1 l= k+ 1 (9) σ = υα σ (10) f Assuming nomal distibutions: α n m n n f (2 + kl an) + to + tu q w υασ z (11) s nm m m f Due to the cental-limit-theoem, the assumption egading nomal distibutions is cucial only when n is small. Thee is a multiplicative inteaction between υ and α which affects the ight-hand tem of expession (11). Since υ and α ae non-negative a simultaneous incease in tavel time and vaiability can have a lage impact on the buffe size. A decease in tavel speed inceases the aveage time to complete the oute, as seen in the left-hand tem of (11). A decease also inceases the equied buffe, as seen in the ight-hand tem of (11). In all cases, as the numbe of tous inceases, the aveage numbe of customes deceases, and the distance pe tou deceases. Howeve, the absolute ate of decease in the aveage distance pe tou is always less than the ate of incease in the aveage numbe of tous. Links with long tavel times have a significant contibution on the final value of f σ as shown in (9). In tous with a long tavel time fom a DC to a sevice aea that is followed by shot inte-custome tips, the value of the standad deviation is detemined by the ound tip fom/to the depot Constaint Coefficient Fo each custome it is possible to define a dimensionless coefficient φ that can povide an indication of the elative impact of congestion on outing constaints fo each custome. α 2 i / sf + to + tuqi φi ( α, υ) = f w υασ z (12) i

13 Figliozzi 13 Whee the time standad deviation fo the ound tip fom the depot to custome i is defined as: σ f i = + f 2 ( ti ) (2 ρ) When Congestion has a distinct impact on each custome due to its location and sevice chaacteistics. φ i eaches the value of one, it is infeasible to seve custome i with the desied level of sevice z. 5. Sensitivity Analysis To illustate how changes in tavel time affect tou chaacteistics as well as VHT/VKT, a sensitivity analysis based on a eal-wold situation 2 and tou data epoted in the liteatue is pefomed. Tou data fom diffeent cities indicate that the aveage numbe of stops pe tou in uban aeas is equal o geate than 5 stops pe tou: appoximately 6 in Calgay (Hunt and Stefan, 2005), 5.6 in Denve (Holguin-Veas and Patil, 2005), and 6.2 in Amstedam (Vleugel and Janic, 2004). Custome sevice is highly elated to the numbe of opeations to be pefomed and the numbe of pallets/packages to be loaded/unloaded; sevice time can be as shot as a few minutes (package delivey). In Amstedam, unloading/loading time pe stop is 21 minutes on aveage; LTL data fom Sydney indicate a median stop time 30 minutes and an aveage time of appoximately 40 minutes (Figliozzi et al., 2007). Routing scenaios wee constucted assuming a sevice aea of 39.5 squae kilometes containing 30 customes, a maximum tou duation of eight hous ( w = 8), thee diffeent ound tip distances to the depot ( 2 = 25, 50, and 75 kilometes), fou diffeent coefficient of vaiations (υ = 0.0, 0.2, 0.4, and 0.6), and fou custome sevice times anging fom 15 to 60 minutes ( t o + t u q =15, 30, and 45 minutes). The coefficient z was set to a 1.64 value. Tous wee designed using a constuction and impovement outing heuistics fo thee aveage speeds: 50, 25 and 12.5 km/h. When congestion sets in, outes must be edesigned to satisfy tou duation constaints as indicated by expessions (4), (5), and (11). Routes 2 Tou chaacteistics and scenaios ae based on data pesented in Figliozzi et al. (2007). The sevice aea epesents the industial distict of Bankstown in the city of Sydney, Austalia.

14 Figliozzi 14 wee built using a VRP constuction and impovement heuistic that povides solutions within 3% of the best solutions fo standad benchmak VRP instances with time window constaint (Figliozzi, 2008a). Using linea egession expession (1) was estimated and the egession fit was R 2 = << Inset Table 1 Hee >> The sensitivity to congestion as a function of custome sevice time is pesented in Table 1. A tou stats at a depot, visits one o moe customes, and then etuns to the depot. Table 1 does not pesent the numbe of tous but the aveage 3 incease factos with espect to fee-flow speed and assuming 2 = 25 km, s = 50, and a constant sevice time pe custome. Fo example, keeping the sevice time constant, t c = 45 min, but educing the speed by half ( s = 25km/h), the numbe of tous needed is 1.25 times lage than the numbe of tous needed when s = 50 km/h. A eduction of tavel speed has a significant effect on VKT and VHT. The impact of congestion on VKT and VHT is highe when customes have longe sevice times. The coesponding constaint coefficients follow a simila tend as shown in Table 2. << Inset Table 2 Hee >> The sensitivity to congestion as a function of distance to the depot is pesented in Table 3; this table is oganized by the thee etun distances (25, 50, 75 km) to depot 2. Each of the sections contains the aveage 4 incease factos with espect to fee-flow speed and no vaiability, i.e. s = 3 The aveage among the thee vaiability factos: 0.2, 0.4, and The aveage among thee custome times t : 15, 30, and 45 minutes c

15 Figliozzi 15 50, υ = 0.0, and fo a given etun distance to depot 2. Fo example, by setting 2 = 50km, the numbe of tous needed when speed is halved ( s = 25km/h) and vaiability inceases fom υ = 0.0 to υ = 0.6 is 1.60 times lage than the numbe of tous needed when s = 50 km/h, and υ = 0.0. << Inset Table 3 Hee >> Seveal obsevations can be made fom the analysis of Table 3: (a) ound tip distance to the depot is a cucial facto. The impact of congestion is amplified as the depot moves futhe away fom its customes; (b) vaiability is an impotant facto fo tavel times that ae elatively long with espect to the tou duation. Fo shot aveage distances to/fom the depot and high speeds the buffe is too small with espect to w and the impact of vaiability is negligible; (c) when congestion is high, i.e. low speeds and high vaiability, it becomes infeasible to seve moe distant customes with a high sevice level; (d) in all cases, the incease in the numbe of tous is geate than the incease in total distance taveled. Hence, the distance pe tou deceases as congestion inceases, i.e. tous become shote on aveage; and (e) as congestion inceases, the numbe of tous needed inceases and with it the pecentage of time diving and the aveage distance pe custome. The coesponding constaint coefficients follow a simila tend as shown in Table 4. << Inset Table 4 Hee >> As shown in Table 2 and Table 4, the analysis of the constaint coefficients poxy to study the sensitivity of tous to changes in congestion levels. φ i is a fast and effective

16 Figliozzi 16 Conceptually, the impact of congestion on VKT/VHT can be analyzed as a function of the custome distance to the depot and the level of the constaint coefficient φ i, see Table 5. When congestion is such that the constaint coefficients ae close to o above one and custome sevice level has to be maintained, new depots ae equied o the sevice of customes located fa away fom the depot must be tansfeed to anothe tanspot povide, fo example a thid paty logistics company (3PL). << Inset Table 5 Hee >> 6. Impact on Costs In tanspot o highway planning studies, commute/passenge congestion costs ae taditionally estimated as the sum of thee diffeent components: 1) the poduct of the tavel time delays and the value of time pe vehicle-dive, 2) a cost due to tavel time uneliability, and 3) highe opeating and envionmental costs. Caies costs ae hade to quantify; the impact of congestion is heavily dependent on netwok (e.g. depot location), oute type (e.g. numbe of stops and its density) and custome sevice chaacteistics (e.g. time windows) that may geatly vay among caies. Congestion not only inceases caies costs but also changes the elative weight of daily opeational costs such as fuel and labo needed pe custome. Table 6 pesents congestion elated fuel and wage inceases as a function of tavel speed and its coefficient of vaiation. The column named total incease facto shows the total cost incease using as a base scenaio a tavel time of 50 km/h and no tavel speed

17 Figliozzi 17 vaiation. The columns named sevice time, diving time, and fuel espectively indicate thei shae as a pecentage of the total fuel plus labo costs 5. << Inset Table 6 Hee >> Fo a given numbe of customes seved, total custome sevice time is not affected by congestion i.e. time spent at the customes locations does not change wheeas fuel and wages ae diectly affected by the amount of VHT and VKT. As congestion inceases, labo and fuel costs elated to time and distance diven become dominant. Fom a caie s pespective, the ultimate monetay impact of congestion depends on how much a caie can chage customes o pass on congestion costs along the supply chain. If diect distance between distibution cente and custome location is the main basis to pice tanspot sevices, caies cannot eadily and tanspaently tansfe the costs bought about by congestion. Table 6 does not include costs associated with the inceases in fleet size needed fo the incease in the numbe of tous. In addition, fo a caie opeating in an uban aea, the costs of congestion may be compounded by: (a) custome sevice employee time to handle custome complaints and escheduling issues; (b) stiff penalties due to JIT (just-in-time) late deliveies o the cost of lage time-buffes; (c) capital and opeational costs of eal time infomation systems, sophisticated vehicle outing and tacking softwae needed to mitigate the impact of congestion (Regan and Golob, 1999); (d) toll oad usage to avoid highly congested steets tucks that come on/off main tolled highways seveal times a day to 5 The fuel and labo costs wee calculated using fuel consumption of a medium-size delivey tuck of appoximately thee kilometes pe lite of diesel at a cost of $1.25 pe lite of diesel. Fuel consumption was inceased to account fo lowe fuel efficiency at low speeds and congested diving conditions. Labo cost was assumed as $20 pe dive hou. Retun distance to depot was assumed to be 50 kilometes and the sevice time pe custome 30 minutes. Maintenance costs ae not consideed, howeve, in a pe kilomete basis they ae bound to incease when vehicles ae opeated in congested conditions, e.g. baking system.

18 Figliozzi 18 access diffeent delivey aeas can accue a significant toll cost (Figliozzi et al., 2007, Holguin-Veas et al., 2006); and (e) paking fees and/o the payment of taffic/paking fines in dense uban aeas lacking loading zones (Mois et al., 1998). 7. Empiical Tou Data Classification and Repesentation This section elates the insights of pevious sections to empiical tou data obtained fom a company based in Sydney, Austalia. The company s customes ae located in seveal industial sububs of Sydney and ound tips between the depot and these industial sububs ange between 14 to 40 kilometes. All distances ae based on eal oad netwok distances as taveled by the commecial vehicles. Fo this paticula distibution opeation time windows ae not an oveiding concen; howeve, deliveies must take place within the pomised day. In addition, deliveies have to be caied out within nomal business hous (most customes pefe moning deliveies); theefoe, the stating time of the tou and its duation ae constained to meet this condition. This is clealy evealed in the tou data: 13% of the deliveies took place befoe 8 am, 45% of the deliveies took place befoe 11 am, 76% of the deliveies took place befoe 2 pm, and 99% of the deliveies took place befoe 5 pm. A detailed desciption and analysis of the tou data is pesented in Figliozzi et al. (2007). In many eal-wold distibution outes, to educe distibution costs customes ae seved and clusteed accoding to thei equiements and geogaphical location. At the disaggegate tou level, time diven and distance diven pe custome (o tou) ae highly coelated as shown in Figue 1. << Inset Figue 1 Hee >>

19 Figliozzi 19 Moe insights egading tou chaacteistics and classifications can be obtained plotting pecentage of time diving (in a given tou) and distance taveled pe custome (in a given tou); see Figue 2. The pecentage of time diving ( PTD ) can be expessed as a function of aveage distance taveled pe stop d, the aveage tavel speed s, and sevice time pe custome t c : PTD nd / s d = = nd / s + nt d + ts c c Hence, PTD is not diectly elated to tou duation o total distance tavelled and bette descibes the efficiency of the tou in tems of tou length and duation pe custome seved. Assuming that custome sevice time cannot be educed without educing quality of sevice, PTD can be educed only educing distance tavelled pe custome o inceasing aveage tavel speed. Accoding to thei location in Figue 2 tous can be divided into thee distinct classes; a summay of these tou chaacteistics is shown in Table 7. Class I tous, Figue 2 lowe left, have many stops and a low pecentage of the tou duation is spent diving. The aveage diving speed is low because the pecentage of local and access oads/steets used inceases with the numbe of customes visited. Despite the low aveage tavel speed, tous ae highly efficient fom the distibuto pespective because many customes ae seved diving a shot distance and a low pecentage of time is spent diving. << Inset Figue 2 Hee >> On the uppe ight section of the gaph (Class III), tous have few stops and a high pecentage of the tou duation is spent diving. The tou length is long because customes ae located futhe away fom

20 Figliozzi 20 each othe and/o the depot is fa fom the distibution aea. Tou duation is high and vey few customes can be seved. The aveage diving speed is high because the pecentage of local and access oads/steets used is small and main highways ae used to connect the depot with the distibution aea. Compaing delivey costs, class III tous have a delivey cost pe custome that is appoximately 3 times highe than class I tous. In addition, class III tous ae moe constained; the aveage constaint coefficient fo class I customes is 0.20 wheeas fo class III customes is Class II tous ae not as efficient as class I tous as the aveage distance tavelled pe stop is significantly highe because the density of stops is lowe than in class I tous. Given that the daily design of tous is based on what feight is available on a paticula day, caies cannot always utilize outes that ae tight both in tems of custome locations and total tou duation. In class II tous, moe customes could have been added to the tou if moe demand had mateialized. Finally, on the lowe ight section of the gaph (Class IV o infeasible tous), below the feasibility bounday, thee is an aea whee feasible tous cannot be found at pactical tavel speeds. Fo a given custome time, tou efficiency and the elative weight of time and distance elated costs can be classified based on pecentage of time diving and the aveage distance pe custome. As congestion wosens the elative weight of labo costs wages and ovetime escalates and the popotion of class II and III tous will gow since educed tavel time and lage buffes peclude the design of tight o efficient outes. << Inset Table 7 Hee >> As indicated in sections 4 and 5, the impacts of congestion ae moe sevee in tous that have a elatively long distance between depot and customes and thee is a significant eduction in tavel speed.

21 Figliozzi 21 Given the tou classification pesented in this section, class III tous ae moe exposed to negative congestion impacts: (a) congestion on feeways dastically educes fee-flow tavel speed; (b) the longe distance between depot and customes exacebates the incease in diving tavel time; and (c) using local steets may not be feasible due to thei lowe tavel speed. Despite the simplifying assumptions made in the analytical modeling of congestion impacts to ensue analytical tactability, the intuition and insights obtained can be applied to the chaacteization and analysis of eal-wold tou data and netwoks. Futue eseach effots can study the impacts of congestion using outing algoithms that ae designed to handle time dependent tavel times (Malandaki and Daskin, 1992), time dependent tavel times with window constaints (Ichoua et al., 2003), o moe geneal algoithms that can handle time dependent tavel times with both soft and had time window constaints as well as geneal cost functions (Figliozzi, 2009). 8. Conclusions This eseach analyzes the impact of congestion on commecial vehicle tous. An analytical model, numeical expeiments, and empiical tou data ae used to undestand changes in tou chaacteistics, caies costs, and VKT-VHT. An incease in aveage tavel time inceases not only diving time but also distance taveled. Theefoe, the diect impact on VHT alone is insufficient to descibe the effects of congestion; the impact on VKT must also be consideed. This eseach shows that long tavel time/distance between custome and depot is a cucial facto that exacebates the negative impacts of congestion. Tavel time vaiability is not as significant when the tavel time between the depot and customes is small in elation to the maximum tou duation and when the outes ae not highly constained. Fo each custome, it is possible to define a dimensionless coefficient that povides an indication of the elative impact of congestion on outing constaints. Congestion impacts on caies costs ae also consideable since congestion not only inceases caies opeating costs but also affects caies cost stuctue. As congestion wosens labo costs, wages

22 Figliozzi 22 and ovetime, may outweigh othe opeating costs. The poductivity of the caie can be measued in tems of tou time and distance equied to seve a custome. Pecentage of time diving and the aveage distance taveled pe custome ae tou chaacteistics suitable to indicate the efficiency of an individual tou because they ae diectly elated to diving time and invesely elated to custome time. This pape categoizes tous into thee classes based on tou efficiency and the elative weight of time and distance elated costs. The poposed classification is based on pecentage of time diving and the aveage distance pe custome. In addition fo a given custome time, a feasibility bounday that is a function of pecentage of time diving and aveage distance pe stop can be established. The tou classification and feasibility boundaies ae valuable and intuitive paametes that epesent eal-wold tou data and classify tous in egads to thei sensitivity to congestion Acknowledgements The autho gatefully acknowledges the Oegon Tanspotation, Reseach and Education Consotium (OTREC) fo sponsoing this poject. This wok was also suppoted by the Depatment of Civil and Envionmental Engineeing in the Maseeh College of Engineeing and Compute Science at Potland State Univesity. Any eos o omissions ae the sole esponsibility of the autho.

23 Figliozzi 23 Refeences BEARWOOD, J., HALTON, H. & HAMMERSLEY, J. (1959) The Shotest Path Though Many Points. Poceedings of the Cambidge Philosophical Society 55, BODIN, L., MANIEZZO, V. & MINGOZZI, A. (2003) Steet Routing and Scheduling Poblems. IN HALL, R. W. (Ed.) Handbook of Tanspotation Science, 2nd Edition. Nowell, Ma., Kluwe Academic Publishes. BREMMER, D., COTTON, K. C., COTEY, D., PRESTRUD, C. E. & WESTBY, G. (2004) Measuing congestion - Leaning fom opeational data. TRANSPORTATION RESEARCH RECORD (1895), CAMBRIDGE SYSTEMATICS (2003) Accounting fo Commecial Vehicles in Uban Tanspotation Models - Task 3 - Magnitude and Distibution. pepaed fo Fedeal Highway Administation- pepaed by Cambidge Systematics, Inc.Cambidge, MA. CHEN, C., SKABARDONIS, A. & VARAIYA, P. (2003) Tavel-time eliability as a measue of sevice. Tanspotation Reseach Recod 1855, DAGANZO, C. F. (1984) The Distance Taveled To Visit N-Points With A Maximum Of C-Stops Pe Vehicle - An Analytic Model And An Application. Tanspotation Science, 18, DAGANZO, C. F. (1991) Logistics Systems-Analysis. Lectue Notes In Economics And Mathematical Systems, 361, ERERA, A. (2000) Design of Lage-Scale Logistics Systems fo Uncetain Envionments. Ph D dissetation, Univesity of Califonia-Bekeley. FIGLIOZZI, M. (2008a) An Iteative Route Constuction and Impovement Algoithm fo the Vehicle Routing Poblem with Soft and Had Time Windows. Applications of Advanced Technologies in Tanspotation (AATT) 2008 Confeence Poceedings. Athens, Geece, May FIGLIOZZI, M. (2009) A Route Impovement Algoithm fo the Vehicle Routing Poblem with Time Dependent Tavel Times. Poceeding of the 88th Tanspotation Reseach Boad Annual Meeting CD om- Januay Washington DC. USA. Washington, DC, Januay FIGLIOZZI, M. A. (2006) Modeling the Impact of Technological Changes on Uban Commecial Tips by Commecial Activity Routing Type. Tanspotation Reseach Recod 1964, FIGLIOZZI, M. A. (2007) Analysis of the efficiency of uban commecial vehicle tous: Data collection, methodology, and policy implications. Tanspotation Reseach Pat B, 41, FIGLIOZZI, M. A. (2008b) Planning Appoximations to the aveage length of vehicle outing poblems with time window constaints. Fothcoming Tanspotation Reseach pat B. FIGLIOZZI, M. A. (2008c) Planning Appoximations to the Aveage Length of Vehicle Routing Poblems with Vaying Custome Demands and Routing Constaints. Tanspotation Reseach Recod 2089, 1-8. FIGLIOZZI, M. A., KINGDON, L. & WILKITZKI, A. (2007) Analysis of Feight Tous in a Congested Uban Aea Using Disaggegated Data: Chaacteistics and Data Collection Challenges. Poceedings 2nd Annual National Uban Feight Confeence, Long Beach, CA. Decembe. GOLOB, T. F. & REGAN, A. C. (2001) Impacts of highway congestion on feight opeations: peceptions of tucking industy manages. Tanspotation Reseach Pat A-Policy And Pactice, 35, GOLOB, T. F. & REGAN, A. C. (2003) Taffic congestion and tucking manages' use of automated outing and scheduling. Tanspotation Reseach Pat E-Logistics And Tanspotation Review, 39, GOLOB, T. F. & REGAN, A. C. (2005) Tucking industy pefeences fo tavele infomation fo dives using wieless Intenet-enabled devices. Tanspotation Reseach Pat C-Emeging Technologies, 13, GREAVES, S. & FIGLIOZZI, M. (2008) Uban Commecial Vehicle Tou Data Collection Using Passive GPS Technology: Issues And Potential Applications. Tanspotation Reseach Recod 2049, HENSHER, D. A. & PUCKETT, S. M. (2005) Refocusing the modelling of feight distibution: Development of an economic-based famewok to evaluate supply chain behaviou in esponse to congestion chaging. Tanspotation, 32, HOLGUIN-VERAS, J. & PATIL, G. (2005) Obseved Tip Chain Behavio of Commecial Vehicles. Tanspotation Reseach Recod 1906, HOLGUIN-VERAS, J., WANG, Q., XU, N., OZBAY, K., CETIN, M. & POLIMENI, J. (2006) The impacts of time of day picing on the behavio of feight caies in a congested uban aea: Implications to oad picing. Tanspotation Reseach Pat A-Policy And Pactice, 40, HUNT, J. & STEFAN, K. (2005) Tou-based micosimulation of uban commecial movements. pesented at the 16th Intenational Symposium on Tanspotation and Taffic Theoy (ISTTT16), Mayland, July 2005.

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25 Figliozzi 25 Tables Table 1 Aveage Incease Factos fo diffeent custome sevice times ( t c ) Aveage Speed Sevice Time ( t c ) 15 min 30 min 45 min Tous Diving Time 50 km/h Distance Tous Diving Time 25 km/h Distance Tous Diving Time 12.5 km/h Distance Table 2 Constaint coefficients φ i assuming υ = 0.0 Aveage Speed Sevice Time ( t c ) 15 min 30 min 45 min 50 km/h km/h km/h

26 Figliozzi 26 Table 3 Aveage Incease Factos fo Diffeent Custome-depot distances ( 2 ) Distance to Depot Coefficient of Aveage Tou Speed ( 2 ) Vaiation 50 km/h 25 km/h 12.5 km/h Tous Diving Time Distance km Tous Diving Time Distance Tous Diving Time Distance km Tous Diving Time Distance Tous Diving Time Distance km Tous Infeasible Diving Time fo z=1.64 Distance

27 Figliozzi 27 Table 4 Constaint coefficients assuming υ = 0.0 Distance to Depot Aveage Speed 50 km/h 25 km/h 12.5 km/h 25 km km km Table 5 Conceptual Impact of Congestion on VKT/VHT Distance to Depot Shot Medium Long Vey High Constaint Coefficient Low High Low Medium High Vey High Appoaching Infeasibility Appoaching Infeasibility Use 3PL o New Depot Table 6 Impact of Congestion on Tou Costs Aveage Tou Speed 50 km/h 25 km/h 12.5 km/h Coefficient Total Sevice Diving of incease Time Time Vaiation Facto Fuel % 13% 27% % 14% 28% % 24% 32% % 27% 36% % 40% 40% % 47% 45%

28 Figliozzi 28 Table 7 Summay of Tou Chaacteistics by Class (Aveages) Tou Class % Time Diving Dist. pe stop (km) Stops pe Tou Tou Duation (h) Tou Distance (km) Tou Speed (km/h) Effective Tou Speed (km/h) Class I 43% Class II 58% Class III 65%

29 Figliozzi 29 Figues 160 Time Diven pe Stop (min) y = 1.384x R² = Distance Tavelled pe Stop (km) Figue 1 Time and Distance pe Custome Seved 90% 80% 70% II. FEWER STOPS LARGER DELIVERY AREA III. FEWEST STOPS FARTHER AWAY FROM DEPOT % Tou Time Diving 60% 50% 40% 30% 20% 10% 0% I. MANY STOPS IV. INFEASIBLE REGION Avg Distance Pe Stop (Km) Figue 2 - Tou Classification by Pecentage Time Diving and Distance Taveled pe Stop